How to use the Volume Calculator (Cube, Cylinder, Cone, Sphere)
- Choose the shape: cube, box, cylinder, cone or sphere.
- Fill in the dimensions named for that shape. Fields for other shapes are ignored.
- Read the volume and surface area.
- Convert units afterwards if needed, for example 1,000 cm³ is 1 litre.
Formula used
Cube a³; box l × w × h; cylinder πr²h; cone πr²h ÷ 3; sphere 4⁄3 πr³. Surface areas: 6a²; 2(lw + lh + wh); 2πr(r + h); πr(r + √(r² + h²)); 4πr².
Worked example
Here is the Volume Calculator (Cube, Cylinder, Cone, Sphere) worked through with the example values shown above, so you can check each step by hand.
| Inputs | |
|---|---|
| Shape | Cylinder |
| Side (cube) | 4 |
| Length (box) | 5 |
| Width (box) | 3 |
| Height (box, cylinder, cone) | 10 |
| Radius (cylinder, cone, sphere) | 3 |
| Result | |
| Volume | 282.74334 |
| Total surface area | 245.04423 |
| Formula used | π × r² × h |
The formulas
A cube with side a has volume a³ and surface area 6a². Side 4 gives 64 and 96. A box is length × width × height, so 5 × 3 × 10 gives 150 with surface area 190.
A cylinder is πr²h: radius 3 and height 10 give 282.74, and the surface area 2πr(r + h) is 245.04. A cone is one third of the cylinder with the same base and height, 94.25 here. A sphere of radius 3 has volume 4⁄3πr³ = 113.1 and surface area 4πr² = 113.1.
Units and capacity
If the dimensions are in centimetres, the volume is in cubic centimetres. One litre equals 1,000 cm³, and one millilitre equals 1 cm³. One cubic metre is 1,000 litres. In US units, a cubic foot is about 7.48 US gallons.
The cylinder above holds 282.74 cm³ if the dimensions are in cm, which is 0.283 litres. The volume converter on this site changes between litres, gallons, cups and more.
Solid shapes in practice
Cylinders describe tanks, pipes, cans and water bottles. Boxes describe rooms, containers and fish tanks. To find how much concrete a rectangular slab needs, multiply length, width and thickness, in the same unit, and then add a margin for waste.
A sphere gives the most volume for a given surface area, which is why bubbles and droplets are round. Cones turn up in funnels, piles of sand and traffic cones, and a pyramid has the same one-third rule.
Checking your work
Use the same unit for every dimension before you start. Mixing centimetres and metres is the most common source of mistakes. Remember that the radius is half the diameter, so if you know the diameter, halve it first.
For a hollow object, such as a pipe, find the volume of the outer shape and subtract the volume of the inner space. This calculator returns the total surface area, including the ends of a cylinder and the base of a cone.
Frequently asked questions
What is the volume of a cylinder?
π × radius² × height. A radius of 3 and height of 10 give about 282.74 cubic units.
How do I convert cubic centimetres to litres?
Divide by 1,000. So 282.74 cm³ is 0.283 litres.
Why is a cone one third of a cylinder?
It is a geometric result: a cone fills exactly one third of the cylinder with the same base and height.
Do I need to fill in every field?
No. The calculator uses only the fields named for your shape.
What does total surface area include?
All outer faces: for a cylinder the curved side and both circular ends, and for a cone the curved side and the base.
What if I know the diameter?
Halve it to get the radius and enter that.
This calculator gives estimates for information only. Actual figures from a bank, employer, tax authority or doctor may differ. It is not financial, tax, legal or medical advice.